By numerical simulations on frequency dependence of the spiking threshold, i.e. on the critical amplitude of periodic stimulus, for a neuron to fire, we find that bushy cells in the cochlear nuclear exhibit frequency selectivity behaviour. However, the selective frequency band of a bushy cell is far away from that of the preferred spectral range in human and mammal auditory perception. The mechanism underlying this neural activity is also discussed. Further studies show that the ion channel densities have little impact on the selective frequency band of bushy cells. These findings suggest that the neuronal behaviour of frequency selectivity in bushy cells at both the single cell and population levels may be not functionally relevant to frequency discrimination. Our results may reveal a neural hint to the reconsideration on the bushy cell functional role in auditory information processing of sound frequency.